We did that in 11th grade pre-calculus class. We got the number 2.71828 and then our teacher said "Now go to that button on your graphing calculator that says

We did that in 11th grade pre-calculus class. We got the number 2.71828 and then our teacher said "Now go to that button on your graphing calculator that says e^x and type e^1" We did and our minds were blown. Why was this strange number that we "discovered" in our calculator already? A few months later I talked to a super advanced math genius kid who had a signature that said e^(i*pi)+1=0 and I asked him if that was Euler's number. He was a super quiet skittish guy that rarely talked. His eyes lit up and he spent the next 2 hours teaching me about Taylor series and showed me how to prove it. It remains the most fascinating math equation I have ever seen. He had a lot of issues and dropped out because he couldn't pass a history class. I found that guy on Facebook 20 years later and thanked him. He didn't remember that but he was so happy that he made such a big impact on me.